If you allowed the potting mix to dry out completely 'a little water' may not have been enough. Potting mixes become water-repellent when allowed to dry out completely, making the moisture unavailable to the plant's roots.

Fill a bucket with water, and immerse your plant, pot and all, into it until all air bubbles cease. Drain well. Hopefully this rehydration of the soil will bring your plant back to life. If you haven't left it too late.

Despite what the books tell you, lavender can take quite a lot of water, as long as it is very well drained. It's not until it become fully mature that it can cope with long periods of drought. It won't tolerate constantly wet feet at any time.

Is your plant getting any natural sunlight - not filtered sunlight through glass, but the Real Thing? That will help.

Lavenders can tolerate cold and frost.
I don't know if French variety is any diiferen though.
I bought one last December from nursery too and planted it right in the garden then. After that we've had snow, cold and temps down to teens and my laveder is doing great. Of course I am in zone 8. But in zone 6 in April should be much warmer than in December in zone 8.